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<span class="Comment">/*</span><span class="Comment">*************************************************************************\</span>

<span class="Comment">MODULE: vec_RR</span>

<span class="Comment">SUMMARY:</span>

<span class="Comment">Defines the class vec_RR.</span>

<span class="Comment">\*************************************************************************</span><span class="Comment">*/</span>


<span class="Type">typedef</span> Vec&lt;RR&gt; vec_RR; <span class="Comment">// backward compatibility</span>

<span class="Type">void</span> mul(vec_RR&amp; x, <span class="Type">const</span> vec_RR&amp; a, <span class="Type">const</span> RR&amp; b);
<span class="Type">void</span> mul(vec_RR&amp; x, <span class="Type">const</span> vec_RR&amp; a, <span class="Type">double</span> b);

<span class="Type">void</span> mul(vec_RR&amp; x, <span class="Type">const</span> RR&amp; a, <span class="Type">const</span> vec_RR&amp; b);
<span class="Type">void</span> mul(vec_RR&amp; x, <span class="Type">double</span> a, <span class="Type">const</span> vec_RR&amp; b);
<span class="Comment">// x = a * b</span>


<span class="Type">void</span> add(vec_RR&amp; x, <span class="Type">const</span> vec_RR&amp; a, <span class="Type">const</span> vec_RR&amp; b);
<span class="Comment">// x = a + b</span>

<span class="Type">void</span> sub(vec_RR&amp; x, <span class="Type">const</span> vec_RR&amp; a, <span class="Type">const</span> vec_RR&amp; b);
<span class="Comment">// x = a - b</span>

<span class="Type">void</span> clear(vec_RR&amp; x);
<span class="Comment">// x = 0 (length unchanged)</span>

<span class="Type">void</span> negate(vec_RR&amp; x, <span class="Type">const</span> vec_RR&amp; a);
<span class="Comment">// x = -a</span>

<span class="Type">long</span> IsZero(<span class="Type">const</span> vec_RR&amp; a);
<span class="Comment">// test if a is the zero vector</span>


<span class="Type">void</span> InnerProduct(RR&amp; x, <span class="Type">const</span> vec_RR&amp; a, <span class="Type">const</span> vec_RR&amp; b);
<span class="Comment">// x = inner product of a and b, padded with zeros to make the lengths</span>
<span class="Comment">// even.</span>

<span class="Type">void</span> VectorCopy(vec_RR&amp; x, <span class="Type">const</span> vec_RR&amp; a, <span class="Type">long</span> n);
vec_RR VectorCopy(<span class="Type">const</span> vec_RR&amp; a, <span class="Type">long</span> n);
<span class="Comment">// x = a copy of a of length exactly n.</span>
<span class="Comment">// The input is truncated or padded with zeroes, as necessary.</span>


<span class="Comment">// operator notation:</span>

vec_RR <span class="Statement">operator</span>+(<span class="Type">const</span> vec_RR&amp; a, <span class="Type">const</span> vec_RR&amp; b);
vec_RR <span class="Statement">operator</span>-(<span class="Type">const</span> vec_RR&amp; a, <span class="Type">const</span> vec_RR&amp; b);

vec_RR <span class="Statement">operator</span>-(<span class="Type">const</span> vec_RR&amp; a);


<span class="Comment">// vector/scalar multiplication:</span>

vec_RR <span class="Statement">operator</span>*(<span class="Type">const</span> vec_RR&amp; a, <span class="Type">const</span> RR&amp; b);
vec_RR <span class="Statement">operator</span>*(<span class="Type">const</span> vec_RR&amp; a, <span class="Type">double</span> b);

vec_RR <span class="Statement">operator</span>*(<span class="Type">const</span> RR&amp; a, <span class="Type">const</span> vec_RR&amp; b);
vec_RR <span class="Statement">operator</span>*(<span class="Type">double</span> a, <span class="Type">const</span> vec_RR&amp; b);

<span class="Comment">// inner product:</span>

RR <span class="Statement">operator</span>*(<span class="Type">const</span> vec_RR&amp; a, <span class="Type">const</span> vec_RR&amp; b);


<span class="Comment">// assignment operator notation:</span>

vec_RR&amp; <span class="Statement">operator</span>+=(vec_RR&amp; x, <span class="Type">const</span> vec_RR&amp; a);
vec_RR&amp; <span class="Statement">operator</span>-=(vec_RR&amp; x, <span class="Type">const</span> vec_RR&amp; a);

vec_RR&amp; <span class="Statement">operator</span>*=(vec_RR&amp; x, <span class="Type">const</span> RR&amp; a);
vec_RR&amp; <span class="Statement">operator</span>*=(vec_RR&amp; x, <span class="Type">double</span> a);


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